Open the Phone app
Tap Voicemail
Select the voicemail message
Tap Delete or the trash icon
Confirm deletion if prompted
Repeat for any other messages
Open the Voicemail tab or app from your carrier if needed
Press and hold 1 to access voicemail if required
Follow the prompts to delete saved messages
Clear voicemail notifications from the notification shade if needed
Restart the Phone app if deleted messages still appear
Contact your carrier if voicemail cannot be cleared